Boundary conditions, effective action, and Virasoro algebra for AdS₃

Abstract

We construct an effective action of General Relativity for small excitations from asymptotic transformations and use it to study conformal symmetry in the boundary of AdS3. By requiring finiteness of the boundary effective action(s) for certain asymptotic transformations, we derive the well known Virasoro algebra and central charge associated with the boundary of AdS3. Our Virasoro generating transformations are asymptotic symmetries of appropriately defined new asymptotically AdS3 spaces which are relaxed compared to the standard Brown-Henneaux ones but which yield the same asymptotic symmetry group and central charge. Thus one may view the effective action approach proposed in this thesis as a method for deriving boundary conditions for an asymptotic symmetry group. However, most importantly, we believe that the effective action approach is by itself an alternative independent way of obtaining and studying asymptotic conformal symmetry in the boundary of certain space-times based on well-grounded requirements of finite action.